Characteristic Vector Fields of Generic Distributions of Corank 2
Jakubczyk, B. ; KryńSki, W. ; Pelletier, F.
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009), p. 23-38 / Harvested from Numdam
@article{AIHPC_2009__26_1_23_0,
     author = {Jakubczyk, B. and Kry\'nSki, W. and Pelletier, F.},
     title = {Characteristic Vector Fields of Generic Distributions of Corank 2},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {26},
     year = {2009},
     pages = {23-38},
     doi = {10.1016/j.anihpc.2007.05.006},
     mrnumber = {2483811},
     zbl = {1154.53018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2009__26_1_23_0}
}
Jakubczyk, B.; KryńSki, W.; Pelletier, F. Characteristic Vector Fields of Generic Distributions of Corank 2. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) pp. 23-38. doi : 10.1016/j.anihpc.2007.05.006. http://gdmltest.u-ga.fr/item/AIHPC_2009__26_1_23_0/

[1] Agrachev A., Methods of Control Theory in Nonholonomic Geometry, in: Zurich 1994, Proc. Int. Congress of Math., vol. 2, Birkhäuser, Basel, 1995, pp. 1473-1483. | MR 1404051 | Zbl 0848.93012

[2] Agrachev A., Sarychev A., Abnormal Sub-Riemannian Geodesics: Morse Index and Rigidity, Ann. Inst. H. Poincaré, Anal. Non Lineaire 13 (6) (1996) 635-690. | Numdam | MR 1420493 | Zbl 0866.58023

[3] Bismut J. M., Large Deviations and the Malliavin Calculus, Birkhäuser, 1984. | MR 755001 | Zbl 0537.35003

[4] Bryant R. L., Hsu L., Rigidity of Integral Curves of Rank 2 Distributions, Invent. Math. 114 (1993) 435-461. | MR 1240644 | Zbl 0807.58007

[5] Chitour Y., Jean F., Trélat E., Genericity Results for Singular Curves, J. Differential Geom. 73 (2006) 45-73. | MR 2217519 | Zbl 1102.53019

[6] Jakubczyk B., Przytycki F., Singularities of K-Tuples of Vector Fields, Dissertationes Math. 213 (1984) 1-64, Warsaw. | MR 744876 | Zbl 0565.58007

[7] Jakubczyk B., Zhitomirskii M., Distributions of Corank 1 and Their Characteristic Vector Fields, Trans. Am. Math. Soc. 355 (2003) 2857-2883. | MR 1975403 | Zbl 1022.58002

[8] Kryński W., Singular Curves Determine Generic Distributions of Corank at Least 3, J. Dynamical Control Syst. 11 (3) (2005) 375-388. | MR 2147191 | Zbl 1088.58003

[9] Liu W., Sussmann H., Shortest Paths for Sub-Riemannian Metrics on Rank 2 Distributions, Mem. Amer. Math. Soc. 118 (564) (1995). | MR 1303093 | Zbl 0843.53038

[10] Montgomery R., Abnormal Minimizers, SIAM J. Control Optim. (1994). | MR 1297101 | Zbl 0816.49019

[11] Montgomery R., A Survey on Singular Curves in Sub-Riemannian Geometry, J. Dynam. Control Syst. 1 (1) (1995) 49-90. | MR 1319057 | Zbl 0941.53021

[12] Pelletier F., Singularités Génériques Des Distributions De Codimension 2 Et Structures Bihamiltoniennes, Bull. Sci. Math. 125 (3) (2001) 197-234. | MR 1822688 | Zbl pre01675760

[13] Rayner C. B., The Exponential Map for the Lagrange Problem on Differentiable Manifolds, Philos. Trans. R. Soc. London. Ser. A Math. Phys. Sci. 262 (1127) (1967) 299-344. | MR 247552 | Zbl 0154.37004

[14] Sussmann H. J., An Introduction to the Coordinate-Free Maximum Principle, in: Jakubczyk B., Respondek W. (Eds.), Geometry of Feedback and Optimal Control, Pure and Applied Math., vol. 207, Marcel Dekker, New York, 1998, pp. 463-557. | MR 1493021 | Zbl 0925.93135

[15] Ślebodziński W., Formes Extérieures Et Leurs Applications, Monografie Matematyczne, vol. 31, Polish Scientific Publishers, Warszawa, 1954. | Zbl 0057.13204

[16] Vershik A. M., Gershkovitch V. Ya., An Estimate of Functional Dimension for Orbits of Germs of Generic Distributions, Matem. Zametki 44 (1988) 596-603. | Zbl 0667.58003

[17] Zhitomirskii M., Typical Singularities of Differential 1-Forms and Pfaffian Equations, Translations of Math. Monographs, vol. 113, AMS, Providence, 1992. | MR 1195792 | Zbl 0771.58001